Differential Equations : Multi-step Methods

Study concepts, example questions & explanations for Differential Equations

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Numerical Solutions Of Ordinary Differential Equations

The two-step Adams-Bashforth method of approximation uses the approximation scheme .

Given that  and , use the Adams-Bashforth method to approximate  for  with a step size of 

Possible Answers:

Correct answer:


In this problem, we're given two points, so we can start plugging in immediately. If we were not, we could approximate  by using the explicit Euler method on .

Plugging into  , we have


Note, our approximation likely won't be very good with such large a time step, but the process doesn't change regardless of the accuracy.


Learning Tools by Varsity Tutors